Tent space well-posedness for parabolic Cauchy problems with rough coefficients
Tài liệu tham khảo
Aronson, 1967, Bounds for the fundamental solution of a parabolic equation, Bull. Am. Math. Soc., 73, 890, 10.1090/S0002-9904-1967-11830-5
Auscher, 2007, On necessary and sufficient conditions for Lp-estimates of Riesz transforms associated to elliptic operators on Rn and related estimates, Mem. Am. Math. Soc., 186
Auscher, 2019, On regularity of weak solutions to linear parabolic systems with measurable coefficients, J. Math. Pures Appl. (9), 121, 216, 10.1016/j.matpur.2018.08.002
Auscher, 2020, L2 well-posedness of boundary value problems for parabolic systems with measurable coefficients, J. Eur. Math. Soc., 22, 2943, 10.4171/JEMS/980
Auscher, 2001, The solution of the Kato square root problem for higher order elliptic operators and systems on Rn, J. Evol. Equ., 1, 361, 10.1007/PL00001377
Auscher, 2012, Singular integral operators on tent spaces, J. Evol. Equ., 12, 741, 10.1007/s00028-012-0152-4
Auscher, 2019, On existence and uniqueness for non-autonomous parabolic Cauchy problems with rough coefficients, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5), 19, 387
Auscher, 2000, Equivalence between regularity theorems and heat kernel estimates for higher order elliptic operators and systems under divergence form, J. Funct. Anal., 177, 310, 10.1006/jfan.2000.3643
Auscher, 1998, Square root problem for divergence operators and related topics, Astérisque, 249
Barton, 2016, Gradient estimates and the fundamental solution for higher-order elliptic systems with rough coefficients, Manuscr. Math., 151, 375, 10.1007/s00229-016-0839-x
Bernicot, 2016, Gaussian heat kernel bounds through elliptic Moser iteration, J. Math. Pures Appl. (9), 106, 995, 10.1016/j.matpur.2016.03.019
Björn, 2011, Nonlinear Potential Theory on Metric Spaces, vol. 17
Blunck, 2005, Generalized Gaussian estimates and the Legendre transform, J. Oper. Theory, 53, 351
Bögelein, 2008, Higher integrability for weak solutions of higher order degenerate parabolic systems, Ann. Acad. Sci. Fenn., Math., 33, 387
Campanato, 1964, Proprietà di una famiglia di spazi funzionali, Ann. Sc. Norm. Super. Pisa (3), 18, 137
Cao, 2016, Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators, Forum Math., 28, 10.1515/forum-2014-0127
Cherrier, 2012, Linear and Quasi-Linear Evolution Equations in Hilbert Spaces, vol. 135
Coifman, 1985, Some new function spaces and their applications to harmonic analysis, J. Funct. Anal., 62, 304, 10.1016/0022-1236(85)90007-2
Dautray, 1992
Davies, 1995, Uniformly elliptic operators with measurable coefficients, J. Funct. Anal., 132, 141, 10.1006/jfan.1995.1103
de Simon, 1964, Un'applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine, Rend. Semin. Mat. Univ. Padova, 34, 205
Deny, 1954, Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble), 5, 305, 10.5802/aif.55
Dong, 2011, On the Lp-solvability of higher order parabolic and elliptic systems with BMO coefficients, Arch. Ration. Mech. Anal., 199, 889, 10.1007/s00205-010-0345-3
Fefferman, 1972, Hp spaces of several variables, Acta Math., 129, 137, 10.1007/BF02392215
Giaquinta, 1982, On the partial regularity of weak solutions of nonlinear parabolic systems, Math. Z., 179, 437, 10.1007/BF01215058
Grafakos, 2009, Modern Fourier Analysis, vol. 250
Janson, 1983, Elementary characterisations of Morrey-Campanato spaces, 101
John, 1961, On functions of bounded mean oscillation, Commun. Pure Appl. Math., 14, 415, 10.1002/cpa.3160140317
Kenig, 1993, The Neumann problem for elliptic equations with nonsmooth coefficients, Invent. Math., 113, 447, 10.1007/BF01244315
Koch, 2012, Geometric flows with rough initial data, Asian J. Math., 16, 209, 10.4310/AJM.2012.v16.n2.a3
Koch, 2015, Parabolic equations with rough data, Math. Bohem., 140, 457, 10.21136/MB.2015.144463
Koch, 2001, Well-posedness for the Navier–Stokes equations, Adv. Math., 157, 22, 10.1006/aima.2000.1937
Maz'ya, 2011, Sobolev Spaces with Applications to Elliptic Partial Differential Equations Fundamental, vol. 342
Moser, 1964, A Harnack inequality for parabolic differential equations, Commun. Pure Appl. Math., 17, 101, 10.1002/cpa.3160170106
Nash, 1957, Parabolic equations, Proc. Natl. Acad. Sci. USA, 43, 754, 10.1073/pnas.43.8.754
Šneĭberg, 1974, Spectral properties of linear operators in interpolation families of Banach spaces, Mat. Issled., 9, 214
Solonnikov, 1965, On boundary value problems for linear parabolic systems of differential equations of general form, Tr. Mat. Inst. Steklova, 83
Stein, 1993, Harmonic Analysis: Real-Variable Methods, Orthogonality and Oscillatory Integrals, vol. 43